中国科学院数学与系统科学研究院期刊网

15 May 2008, Volume 51 Issue 3
    

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  • Yu Ming CHU(1); Jin Fa CHENG(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 417-422. https://doi.org/10.12386/A2008sxxb0049
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    Let D be a Jordan domain in R~2.In this paper,we prove that D is a b-John disk if and only if there exists a constant c≥1 such that k_D(x_1,x_2)≤cH_D(x_1,x_2) for all x_1,x_2∈D.Here k_D(x_1,x_2) is the quasihyperbolic metric in D,H_D(x_1,x_2)= 1/2log(1+(1(γ)/(d(x_1,■D))))(1+(1(γ)/(d(x_2,■D)))),whereγis the quasi-hyperbolic geodesic which joins x_1 and x_2 in D and l(γ) is the Euclidean length ofγ.
  • Hong Guang FU(1); Wei Min WANG(1); Bing Zhen ZENG(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 423-434. https://doi.org/10.12386/A2008sxxb0050
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    The famous mathematician Paul Erd■s once provided an interesting ques- tion:"Let U be a set of circles in the plane such that any line intersects at least one of those circles.Then,for a given natural number m,is there a line in the plane inter- secting at least m circles in U?"This problem is solved by Jingzhong Zhang and Lu Yang etc.This paper discusses the generalization of the question under conic,and gets some similar conclusion.
  • Jian Feng HUANG; Yuan Heng WANG
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 435-446. https://doi.org/10.12386/A2008sxxb0051
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    Suppose E is a Banach space with uniformly normal structure and suppose E also has uniformly Gateaux differentiable norm.Let A be an m-accretive operator such that C = D(A) is a convex subset of E.Let {α_n} be a sequence in the interval (0,1) and let {r_n} be a sequence in the interval (0,∞).Then,under some suitable conditions,the sequence {x_n} defined by (1.2) converges strongly to an element of A~(-1)(0).Secondly,we also prove that:Let E be a uniformly convex Banach space whose norm is Frechet differentiable.Let {α_n},{β_n} be two squences in the interval (0,1) and let {r_n} be a sequence in the interval (0,∞).If A~(-1) (0)∩B~(-1)(0)≠0,then,under some suitable conditions,the sequence {x_n} defined by (3.20) converges weakly to an element in A~(-1)(0)∩B~(-1)(0).Our results extend and improve Theorem 2 of Kamimura, Takahashi (2000) and theorem 4.1,Theorem 4.2,Theorem 4.3 of Xu (2006):(i) In Theorem 2 of Kamimura,Takahashi (2000),the condition"Every bounded,closed and convex subset of a reflexive Banach space has the fixed point property for nonexpansive mappings"is removed;(ii) In Xu H.K.(2006),the condition"E is reflexive and has a weakly continuous duality map J_■"is replaced by"E is a Banach space with uniformly normal structure and E also has uniformly Gateaux differentiable norm."so that it contains some Banach spaces besides the Banach space which is in Xu H.K.(2006). At the same time,we state how to approximate a common zero of two m-accretive operators in E.Hence,the results also improve and unify some corresponding results.
  • De Xiang MA(1); Wei Gao GE(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 447-456. https://doi.org/10.12386/A2008sxxb0052
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    By employing Mawhin's continuation theorem,we obtain the existence of solutions and establish a corresponding iterative scheme for BVP, {(φ_p(u′))′+f(t,u) =0,0≤t≤1,u(0) = 0,u(1) =∑_(i=1)~(m-2)γ_iu(η_i). The upper and lower solutions method and monotone iterative technique are used.Fur- thermore,we impose sufficient conditions on f(t,u) which can guarantee the existence of nonnegative or nonpositive solutions even when f(t,u) is allowed to change sign.
  • Jian Qiang FENG
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 457-468. https://doi.org/10.12386/A2008sxxb0053
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    We study the Lie triple system (L.t.s.) J over a field K admitting a nondenerate invariant symmetric bilinear form (call such a J metrisable).We give the definition of T_ω~*-extension of an L.t.s.J,prove a necessary and sufficient condition for a metrised L.t.s.(J,φ) to be isometric to a T~*-extension of some L.t.s.,and determine when two T~*-extension of an L.t.s.are"same",i.e.they are equivalent or isometrically equivalent.In the end,we prove that any nilpotent metrised L.t.s.is either isometric to some T~*-extension or isometric to a nondegenerate ideal of codimension one in some T~*-extension according to the dimension of the algebra is even or odd when the characteristic of the ground field is equal to 0.
  • Zhi Hui CHEN; Yao Tian SHEN
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 469-474. https://doi.org/10.12386/A2008sxxb0054
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    Using the Ekeland variational principle,we prove the solvability of the first eigenvalue problem for a class of quasilinear elliptic equations including distance potential with homogeneous Dirichlet boundary condition.Furthermore,using critical point theory,we obtain the existence of a nontrivial solution to a class of quasilinear elliptic equations with distance potential.
  • Jian Hua ZHANG; Wei DU
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 475-480. https://doi.org/10.12386/A2008sxxb0055
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    We prove that every Lie derivation on a CSL algebra whose lattice is gen- erated by finitely many commuting independent nests is the sum of an inner derivation and a center-valued linear map sending commutators to zero.
  • Ya Qin WANG
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 481-486. https://doi.org/10.12386/A2008sxxb0056
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    The purpose of this paper is to introduce and study a new class of nonlinear set-valued variational inclusions with C-monotone type mappings in a real reflexive Banach space.And we prove the uniqueness of solutions to this class of set-valued variational inclusions and the convergence of the Ishikawa iteration process with errors for approximating solutions.The result presented in this paper improves and extends many corresponding results obtained by Huang,Fang and others.
  • Wen Gu CHEN(1); Youngsheng HAN(2) Chang Xing MIAO(1)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 487-492. https://doi.org/10.12386/A2008sxxb0057
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    It is well known that Calder6n-Zygmund operators T are bounded on H~p for n/n+∈
  • Li Feng XI(1); Huo Jun RUAN(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 493-500. https://doi.org/10.12386/A2008sxxb0058
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    For two self-similar sets satisfying the stong separation condition,the nec- essary and sufficient condition for them to be Lipschitz equivalent is obtained in terms of graph-directed construction.
  • Yi Sheng SONG; Xin Kuan CHAI
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 501-508. https://doi.org/10.12386/A2008sxxb0059
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    Let K be a nonempty closed convex subset of Banach space E,and T : K→K be a generalized Lipschitz pseudocontractive mapping.For any fixed Lipschitz strong pseudocontractive reaping f:K→K,the sequence {x_n} is given by:For x_1∈K,x_(n+1)= (1-α_n-β_n)x_n+α_nf(x_n)+β_nTx_n.It is shown,under appropriate conditions on the sequences of real numbers {α_n} and {β_n},that {x_n} strongly converges to some fixed point x~* of T whenever {z∈K;μ_n||x_n-z||~2=inf_(y∈Kμ_n)||x_n-y||~2}∩F(T)≠0.
  • Xiao Fei QI(1); Shuan Ping DU(2); Jinchuan Hou(3)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 509-516. https://doi.org/10.12386/A2008sxxb0060
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    Let X be a Banach space over the real or complex field F,let A be a standard operator algebra on X with unit I.Suppose thatΦ:A→A is an additive map and m,n are positive integers.It is proved that,ifΦsatisfiesΦ(A~(m+n+1)) - A~mΦ(A)A~n∈FI for all A∈A,then there exists someλ∈F such thatΦ(A) =λA for all A∈A.The same result is true for additive maps on the space of all self- adjoint operators.In addition,a complete characterization of mapsΦon centrally prime algebras satisfying (m+n)Φ(AB) - mAΦ( B ) - nΦ( A )B∈FI is obtained.
  • Guo Wei ZHANG(1); Jing Xian SUN(2); Tie ZHANG(3)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 517-522. https://doi.org/10.12386/A2008sxxb0061
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    By applying retract in normed linear spaces,we give in this papera fixed point theorem of domain compression and expansion of convex functional type,and extend Guo's theorem.
  • Yin Bin LEI(1); Mao Kang LUO(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 523-528. https://doi.org/10.12386/A2008sxxb0062
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    We investigate retracts of Cartesian product of finite posets,then prove Plotkin's conjecture in 1978.Furthermore,we give a partial answer to an open problem of Mislove and Lawson in"Open Problems in Topology".
  • Cheng Bo ZHAI(1); Wen Xia WANG(2); Ling Ling ZHANG(3)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 529-540. https://doi.org/10.12386/A2008sxxb0063
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    The existence and uniqueness of positive fixed points for a class of gen- eralized concave and convex operators is obtained by means of the properties of cone and monotone iterative technique,and the properties of eigenvalue equations for these operators are also given.As an application,we utilize the results obtained in this pa- per to study the existence and uniqueness of positive solutions for a class of integral equations.
  • Hai Tao LI(1); Jian Bin SU(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 541-548. https://doi.org/10.12386/A2008sxxb0064
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    We discuss the extremal problem on the fourth type of super-Cartan domain Y_(IV)(N;n;k),obtain the extremal mapping and extremal value between the fourth type of super-Cartan domain and the unit ball.
  • Lv Ping CHEN
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 549-558. https://doi.org/10.12386/A2008sxxb0065
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    The author uses the techniques of localization and biholomorphic maps,uti- lizes the relation between Bochner-Martinelli kernel on Stein manifolds and Bochner- Martinelli kernel in Cn,introduces Plemelj formulas of singular integrals and Plemelj formulas for derivatives of Bochner-Martinelli integrals in C~n which shown in papers [7,8],and obtains the Plemelj formulas for derivatives of Bochner-Martinelli integrals on Stein manifolds.
  • Shi Heng LI(1); Wu Jie SHI(2); Deng Feng LIANG(3)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 559-566. https://doi.org/10.12386/A2008sxxb0066
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    We study the influence ofθ-pairs for maximal subgroups and 2-maximal subgroups on the structure of group.Let G be a finite groups.If there exists a maximalθ-pair (C,D) such that MC = G and C,/D is 2-closed for every maximal subgroup M of G,then G is solvable;If there exists a maximalθ-pair (C,D) such that HC = G and C/D is nilpotent for every 2-maximal subgroups H of G,then G is nilpotent.
  • Hua Ying ZHAN
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 567-570. https://doi.org/10.12386/A2008sxxb0067
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    The main result of this paper is about the Mazur-Ulam theorem for non- surjective isometry between two F,-spaces,which is a general case of A.Vogt's result. At the end of the paper is a corollary which improves the result of Skof.
  • Li YANG
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 571-578. https://doi.org/10.12386/A2008sxxb0068
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    We study whether the derivative f~((k)) in Frank-Weissenborn inequality can be replaced by a general linear differential polynomial a_0f+a_1f′+…+ a_kf~((k))or not, and have solvedit completely.As applications of this result,Hayman-Yang inequality and some known theorems are generalized.Examples are provided to show that the conditions of theorems obtained in the present paper are essential.
  • Ding Xing ZHONG; Hong An SUN
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 579-592. https://doi.org/10.12386/A2008sxxb0069
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    Let x:M~n→S~(n+1) be a hypersurface in the (n+1)-dimensional unit sphere S~(n+1) without umbilics.Four basic invariants of x under the Moebius transformation group in S~(n+1) are:a Riemannian metric g called Moebius metric,a 1-formΦcalled Moebius form,a symmetric (0,2) tensor A called Blaschke tensor and a symmetric (0,2) tensor B called Moebius second fundamental form.Li and Wang (2003) have studied the hypersurfaces x :M~n→S~(n+1),which satisfy:(i)Φ= 0,(ii) A +λg +μB = 0 for some functionsλandμ.They have proved thatλandμmust be constants,and have classified the hypersurfaces.In this paper,letting D=A +λB,whereλis a constant,then D is a symmetric (0,2) tensor and a Moebius invariant.D is called para-Blaschke tensor of x,an eigenvalue of the para-Blaschke tensor is called a para- Blaschke eigenvalue of x.We classify the hypersuffaces x :M~n→S~(n+1),which satisfy: (i)Φ= 0,(ii) D has exactly two distinct constant para-Blaschke eigenvalues.
  • Xiao Hong CAO(1); Mao Zheng GUO(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 593-600. https://doi.org/10.12386/A2008sxxb0070
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    If ||Tx||~2≤||T~2x||·||x|| for every x∈H,T∈B(H) is called a paranormal operator.T∈B(H) is called"algebraically paranormal"if p(T) is paranormal for some nonconstant complex polynomial p.In this note,using the spectral characteristic of the algebraically paranormal operator,we study the Weyl's theorem for algebraically paranormal operator and for its quasi-affine transform.
  • Yan Hui ZHAO
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 601-606. https://doi.org/10.12386/A2008sxxb0071
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    The necessary and sufficient conditions are given for the extended Cesàro operator to be bounded and compact fromβ_μspace toβ_v space,fromβ_(μ,0) space toβ_(v,0) space on the unit ball of C~n.
  • Jian Wei ZHAO
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 607-616. https://doi.org/10.12386/A2008sxxb0072
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    The topic of this paper is on the algebraic property and factor classification of the discrete crossed products A_n x_αG_(A,b_1,…b_n) acting on the Euclidean space R~n. Firstly,we show that this crossed product is injective.Secondly,we give some sufficient and necessary condition for the crossed product to be a factor.Lastly,we discuss the factor type of this crossed product when it is a factor.
  • Rui Fang ZHAO; Yong-fei Jin
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 617-624. https://doi.org/10.12386/A2008sxxb0073
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    We study the invariant subspaces of the operator M_z on the Sobolev disk algebra R(D).First,we study the multiplication operator M_z restricted to the invariant subspace.Then we show that M_z restricted to one invariant subspace is unitarily equivalent to M_z restricted to another invariant subspace if and only if the two invariant subspaces are equal.We also characterize the invariant subspaces with common zeros on the boundary of the disk.